1. Field of the Invention
The present invention relates in general to an apparatus and a method for exponential computation, and more particularly to an apparatus and method to precisely calculate an exponential calculating result for a base 2 floating-point number.
2. Description of the Related Art
The representation of floating-point numbers is similar to the commonly used scientific notation and consists of two parts, the mantissa M and the exponent. The floating-point number F represented by the pair (M,E) has the value,F=M×βE
Where β is the base of the exponent.
In an effort to unify methods employed in calculater systems for performing binary floating-point arithmetic, the IEEE in the early 1980's standardized calculater floating-point numbers. Such binary floating-point numbers make possible the manipulation of large as well as small numbers with great precision, and thus are often used in scientific calculations. They typically comprise either single precision format or double precision format, with single precision operating on 32-bit operands and double precision operating on 64-bit operands. Both single and double precision numbers constitute a bit-string characterized by three fields: a single sign bit, several exponent bits, and several fraction or mantissa bits, with the sign bit being the most significant bit, the exponent bits being the next most significant, and the mantissa bits being the least significant.
FIG. 1 is a diagram showing the form of the single format. Since base 2 was selected, a flowing point number F in the single format has the form:F=(−1)S·2E−127·(1.f)
Where                S=sign bit;        E=8-bit exponent biased by 127;        f=F's 23-bit fraction or mantissa which, together with an implicit leading 1, yield the significant digit field “1.--”.         
In present day calculators, the calculation of the floating-point is used for almost all kinds of calculations. Calculator efficiency depends on the efficiency of the calculation of the floating-point. For exponential computation of a floating-point number, an exponential table is usually determined in advance. Then, the result is found by looking up the table. However, when using the exponential table, there is a problem of precision. An 8-bit exponential table is quite large. A memory with large size is required to store the 8-bit exponential table. But if an 8-bit exponential table is used for exponential computation of a floating-point number, the precision of the calculating result is not sufficient. Because the mantissa part of the floating-point number has 23 bits, to precisely calculate an exponent of a floating-point number, an 8-bit exponential table is not enough.